Tailorable stimulated Brillouin scattering in nanoscale
silicon waveguides
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Citation
Shin, Heedeuk, Wenjun Qiu, Robert Jarecki, Jonathan A. Cox,
Roy H. Olsson, Andrew Starbuck, Zheng Wang, and Peter T.
Rakich. “Tailorable stimulated Brillouin scattering in nanoscale
silicon waveguides.” Nature Communications 4 (June 6, 2013). ©
2013 Nature Publishing Group, a division of Macmillan
Publishers Limited
As Published
http://dx.doi.org/10.1038/ncomms2943
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Nature Publishing Group
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Final published version
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Thu May 26 05:12:38 EDT 2016
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http://hdl.handle.net/1721.1/82583
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ARTICLE
Received 6 Sep 2012 | Accepted 29 Apr 2013 | Published 6 Jun 2013
DOI: 10.1038/ncomms2943
OPEN
Tailorable stimulated Brillouin scattering
in nanoscale silicon waveguides
Heedeuk Shin1, Wenjun Qiu2, Robert Jarecki1, Jonathan A. Cox1, Roy H. Olsson III1, Andrew Starbuck1,
Zheng Wang3 & Peter T. Rakich4
Nanoscale modal confinement is known to radically enhance the effect of intrinsic Kerr and
Raman nonlinearities within nanophotonic silicon waveguides. By contrast, stimulated
Brillouin-scattering nonlinearities, which involve coherent coupling between guided photon
and phonon modes, are stifled in conventional nanophotonics, preventing the realization of a
host of Brillouin-based signal-processing technologies in silicon. Here we demonstrate stimulated Brillouin scattering in silicon waveguides, for the first time, through a new class of
hybrid photonic–phononic waveguides. Tailorable travelling-wave forward-stimulated Brillouin
scattering is realized—with over 1,000 times larger nonlinearity than reported in previous
systems—yielding strong Brillouin coupling to phonons from 1 to 18 GHz. Experiments show
that radiation pressures, produced by subwavelength modal confinement, yield enhancement
of Brillouin nonlinearity beyond those of material nonlinearity alone. In addition, such
enhanced and wideband coherent phonon emission paves the way towards the hybridization
of silicon photonics, microelectromechanical systems and CMOS signal-processing
technologies on chip.
1 Sandia National Laboratories, Albuquerque, New Mexico 87185, USA. 2 Department of Physics, Massachusetts Institute of Technology, Cambridge,
Massachusetts 02139, USA. 3 Department of Electrical and Computer Engineering, University of Texas at Austin, Austin, Texas 78758, USA. 4 Department of
Applied Physics, Yale University, New Haven, Connecticut 06520, USA. Correspondence and requests for materials should be addressed to P.R.
(email: peter.rakich@yale.edu).
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P
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hoton–phonon coupling through guided-wave stimulated
Brillouin scattering (SBS) provides a powerful means of
realizing tailorable slow light1,2, radio frequency (RF)–
photonic signal processing3,4, narrow-line-width laser sources5–11,
RF–waveform synthesis12–14 and optical frequency comb
generation12,15,16. Realization of this form of travelling-wave
photon–phonon coupling in a silicon-based and CMOS
(complementary metal–oxide–semiconductor)-compatible platform
could enable high-performance signal-processing applications
through nanoscale Brillouin interactions17,18. Nanoscale modal
confinement has been shown to radically enhance non-linear lightmatter interactions within silicon waveguides19–22 and in nanooptomechanics23–26. For instance, tight optical confinement in
nanoscale silicon waveguides is responsible for greatly enhanced
Raman and Kerr non-linearities19–22,27, and for new sensing23,
actuation23,28,29 and transduction30 mechanisms based on optical
forces within nano-optomechanical systems.
The field of cavity optomechanics has produced a wide variety
of systems with enhanced and controllable forms of photon–
phonon coupling25,31–33. Specifically, silicon-based cavityoptomechanical systems30,34,35 have recently enabled powerful
new forms of quantum state transfer34,36, slow light37, phonon
lasers38 and optomechanical ground-state cooling39. Such cavity
systems exploit resonantly enhanced coupling between discrete
photonic and phononic modes. As a fundamental complement to
cavity systems, guided-wave Brillouin processes produce coupling
between a continuum of photon and phonon modes for a host of
wideband (0.1–34 GHz) RF and photonic signal-processing
applications12,40–43. For example, travelling-wave Brillouin
processes have enabled unique schemes for optical pulse
compression13, pulse and waveform synthesis12,14,15,44, coherent
frequency comb generation12,15,16, variable bandwidth optical
amplifiers44,45, reconfigurable filters46 and coherent beamcombining schemes47. Although there are a variety of
compelling opportunities for chip-scale Brillouin technologies,
to date the observation of Brillouin processes in silicon
nanophotonics has proven difficult; strong Brillouin nonlinearities require large optical forces and tight confinement of
both phonons and photons, conditions that are not met in
conventional silicon waveguides41.
In this paper, we demonstrate travelling-wave forward SBS
nonlinearities and forward SBS gain in silicon waveguides for the
first time through a novel class of hybrid photonic–phononic
waveguides. Confinement of both photons and phonons is
achieved using a Brillouin-active membrane waveguide structure,
eliminating the substrate pathway for phonon losses that stifles
SBS in conventional silicon-on-insulator waveguides. In contrast
to the theoretical work presented in ref. 41, this compoundmaterial waveguide geometry provides independent control of the
photonic and phononic waveguide modes and the resulting
Brillouin spectra. We show that these degrees of freedom enable
the placement of forward SBS resonances between 1 and 18 GHz
through phase-matched coupling to ultra-low group velocityguided acoustic waves. The strength and bandwidth of photon–
phonon coupling is quantitatively studied using heterodyne
four-wave mixing (FWM) techniques and through direct
measurements of Brillouin gain. Experiments reveal that forward
SBS non-linearities surpass those generated by the intrinsic
Raman and Kerr non-linearities in silicon, corresponding to a
Brillouin non-linear coefficient that is more than 1,000 times
greater than prior demonstrations of forward SBS12. The
magnitude and frequency dependence of the Brillouin coupling
show excellent agreement with multi-physics models, revealing
that a coherent combination of electrostrictive (ES) forces48 and
boundary-induced radiation pressures28,49 is responsible for the
enhancement of Brillouin interactions within these nanoscale
2
waveguides. The emergence of strong radiation-pressure-mediated
Brillouin coupling is noteworthy, as it represents a new regime of
Brillouin non-linearity arising from strong boundary interactions in
subwavelength limit of confinement41,48,49. Detailed analysis of the
waveguide nonlinear responses also reveals that a coherent
interference between Kerr and Brillouin non-linearities either
cancel or enhance the total third-order nonlinearity at individual
frequencies.
Results
A Brillouin-active membrane waveguide. Figure 1a is a schematic showing the anatomy of the fabricated Brillouin-active
membrane waveguide (or BAM waveguide). The BAM waveguide
under study is seen in the top-down scanning electron microscopic (SEM) images of Fig. 1c,d, showing a silicon nanophotonic
waveguide embedded within the centre of a series of five suspended phononic waveguide segments. The SEM image in Fig. 1b
shows a cross-section of the waveguide core at one point along
its length. The BAM waveguide consists of a nanoscale
(313 194 nm) silicon waveguide embedded in a tensile silicon
nitride membrane (thickness 124 nm). As illustrated in Fig. 1e,f,
total internal reflection between silicon (n ¼ 3.5) and silicon
nitride (n ¼ 2.0) tightly confines the optical mode to the silicon
waveguide core, here the patterned silicon nitride membrane acts
to guide the generated phonons. This compound-material device
geometry provides independent control of the photonic and
phononic waveguide dispersion, allowing the phonon modes to
be shaped separately from the optical forces within the core of the
silicon waveguide.
Phase-matched coupling via forward SBS. This paper examines
intramodal forward SBS through Brillouin coupling between
guided transverse-electric-like optical modes of the type seen in
Fig. 2b. The computed ES force densities (Fig. 2c–e) and radiation
pressure-induced force densities (Fig. 2f) that mediate Brillouin
coupling are shown in Fig. 2. Through forward SBS, copropagating pump and Stokes waves of frequencies op and os,
respectively, couple through parametrically generated acoustic
phonons of difference frequency O ¼ op os. Momentum conservation requires that k(op) ¼ K(O) þ k(os), where k(o) is the
optical dispersion relation, and K(O) is the phonon-dispersion
relation. Thus, strong photon–phonon coupling is mediated by the
set of phonons, {Oi}, whose dispersion relations satisfy the phasematching condition Dk(O) ¼ k(op) k(op O) ¼ K(O). Vector
representation of this phase-matching condition is seen in Fig. 1g.
The computed dispersion relations of the Brillouin-active phonon
modes guided by a BAM waveguide of width w ¼ 3.8 mm are seen in
Fig. 2h. For further details of the simulation methods, see
Supplementary Note 1. Only the phonon modes that exhibit strong
Brillouin coupling through good overlap between the elastic
displacement fields and the optical force distributions are
shown41,50. The optical wave vector mismatch, Dk(O), is plotted
(red) atop the phononic dispersion relation, K(O), as seen in Fig. 2h.
The points of intersection between these curves (seen as circles)
identify the O- and K-values of the phase-matched phonon modes.
Numerous phase-matched phonon modes are seen with evenly
spaced frequencies spanning 1–16 GHz, and corresponding values of
|K| between 1.3 and 17 rad cm 1. The BAM waveguide consists of a
periodic-array Brillouin-active suspended regions, as seen by the
SEM micrograph of Fig. 1c. As the spatial period of the waveguide
modulation (125 mm) is more than 20 times smaller than the
longitudinal period of the guided phonon wave vector (2p/|K|), the
phase-matching conditions are unaffected.
On the basis of the phase-matching condition and the relation
jDkðOÞj ffi ð@jkj=@oÞ O ¼ ðO=vg Þ, only guided phonons with
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w
z
K
x
y
x
Si3N4
Phononic mode
100 μm
Slot
Si waveguide
kp
z
SiO2
x
ks
Si
y
x
Optical mode
a
K
Si
b
t
Si3N4
K
y
kp
x
ks
kp
ka
Figure 1 | Hybrid photonic–phononic waveguide enabling independent control of the optical and phonon modes. (a) Diagram showing anatomy of
the Brillouin-active membrane waveguide (BAM waveguide). (b) High-resolution SEM cross-section of the silicon waveguide core with width a ¼ 313 nm
and height b ¼ 194 nm within the silicon nitride membrane with thickness t ¼ 124 nm. Scale bar, 200 nm. (c) Top-down SEM image of a portion of the
BAM waveguide displaying a series of five identical membrane-suspended regions. The scale bar is 100 mm. (d) Magnified view of single suspended region
with w ¼ 3.8 mm. (e,f) e and f illustrate propagation of the guided elastic and optical modes respectively within the highlighted section of d. (g) Vector
phase matching diagrams for Stokes and anti-Stokes forward-stimulated Brillouin scattering; kp, ks and ka represent the optical pump, Stokes, and
anti-Stokes wave-vectors; K is the phonon wave-vector.
phase velocities matching the group velocity of light (vg) produce
resonant coupling through forward SBS. This is because the
interference between the copropagating pump and Stokes waves
yields modulated energy density and force density distributions
that propagate along the waveguide at the group velocity (vg) of
light. As this travelling-force distribution drives photon–phonon
coupling, only phonons with phase velocities (O/K) matching the
group velocity (vg) of light can produce efficient coupling (seen as
circles in Fig. 2h). These ultra-high phase-velocity-guided phonon
modes (B108 m s 1) have corresponding guided phonon group
velocities (@O/@K) that are exceedingly slow (B1 m s 1), but are
non-zero.
The displacement field associated with each of the phasematched Brillouin-active guided wave modes is shown in Fig. 2i.
Periodic boundary conditions are applied to the z-normal faces of
this simulation domain to compute the displacement fields of the
phase-matched phonon modes in Fig. 2i and the corresponding
phonon-dispersion curves in Fig. 2h. Although these guided
elastic modes exhibit some flexural character, the vast majority of
the modal potential energy is ascribed to in-plane (x–z) elastic
compression. The compressive character of these slow group
velocity-guided modes is most clearly seen in the high frequency
limit, as demonstrated by the displacement fields of the m ¼ 6 and
m ¼ 7 modes in Fig. 2i. For small K-values, the z-component of
the phonon displacement field becomes much smaller than the
x-component. Moreover, in the limiting case where the
waveguide possesses vertical symmetry (that is, for t ¼ b), these
Brillouin-active modes exactly converge to symmetric Lamb
waves with nearly identical dispersion curves to those seen in
Fig. 2g. Hence, these waves are classified as symmetric Lamb
waves, producing equal frequency spacing of the phase-matched
Brillouin modes seen in Fig. 2h. For further details concerning
mode classification and elastic wave simulation, see Supplementary Note 1.
The waveguides under study have a total length of L ¼ 4.9 mm,
with 26 Brillouin-active membrane-suspended regions spanning a
3.3-mm section of this length. This 3.3 mm Brillouin-active device
length coincides with a total non-linear phase mismatch, |Dk| L,
of between 0.45 and 5.7 radian for the range of Brillouin-active
modes identified in Fig. 2. Previous nano-optomechanical
waveguide systems of shorter length scales have been accurately
treated as lumped-element systems23,24. However, this travellingwave device produces a significant non-linear phase mismatch
along its length. Thus, it is necessary to treat this system as a
phase-matched travelling-wave process to describe coherent
addition of non-linearities along the entire length of the
waveguide as in ref. 12.
Non-linear Brillouin spectroscopy. Through experiments, an
array of BAM waveguides are studied with waveguide widths, w,
between 0.8 and 3.8 mm, producing a wide range of Brillouin
resonances between 1 and 18 GHz. As the optical group velocity,
vg, changes by only a few per cent over a 30-nm wavelength
range, the optical phase mismatch (with values, j Dk j L 2p)
changes to negligible degree over an appreciable wavelength
range. As a consequence, the same guided phonon can be excited
by continuum of different wavelengths within the BAM waveguide despite the fact that it is a phase-matched non-linear process12,18. This property of the system allows pump and probe
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ARTICLE
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y
Si3N4
ES force density (x)
x
ES boundary force
Si
Ex field distribution
ES force density (y)
Max.
0
Max.
RP boundary force
–Max.
y
18
m=7
p
x
m=7
kp
16
Ω
Ω(Δk)
Δk
ks
Frequency Ω/2π (GHz)
14
s
m=5
m=5
12
Ω(K)
10
m=4
m=4
8
m=3
m=3
6
2
0
m=2
m=2
4
k
m=6
m=6
K
m=1
0
m=1
10
20
10 k 20 k
Wave vector (rad cm–1)
Figure 2 | Simulations of hybrid photonic–phononic waveguide. (a,b) The waveguide cross-section and the computed Ex field profile of the optical mode.
(c–f) Computed force distributions associated with the guided optical mode. (c,d) The x and y components of the ES force densities generated within
silicon, respectively. (e,f) ES- and radiation pressure (RP)-induced boundary forces, respectively, produced by the optical mode. (g) Sketch showing the
optical wave vector mismatch, Dk, produced by the dispersion of the optical waveguide mode, o(k), as the pump and stokes waves are detuned. (h)
Dispersion curves showing phonon frequency versus longitudinal wave vector of the Brillouin-active phonon modes for a w ¼ 3.8 mm BAM waveguide. A
break in the scale of the x axis is shown. For small wave vectors (left), the phase-matched phonons (circles) are identified by the intersection between the
optical wave vector mismatch (red) and the Brillouin-active phonon modes (blue). (i) Displacement fields of each of the phase-matched guided-wave
phonon modes identified in h. Each mode is labelled (m ¼ 1,2y7) according to the mode index in h. The right half of each displacement field is shown as
the symmetric force distributions of c–f only permit coupling to phonons with symmetric displacement fields about the waveguide core. Periodic boundary
conditions were applied to the z-normal faces of the simulation domains in i to capture the travelling-wave nature of these guided phonons at the phasematched K-values identified in h.
waves of disparate wavelengths to couple to each other through
the Brillouin-active modes of a single device. To obtain large
Brillouin non-linearities, a serial array of 26 suspended regions
were fabricated along each waveguide, yielding a Brillouin-active
length of 3.3 mm out of a total 4.9 mm device length. Note that
each suspended waveguide section is separated by a 25-mm
anchored (or unsuspended) region.
Experimental studies of Brillouin non-linearity were performed
with the heterodyne FWM apparatus, seen in Fig. 3, yielding
direct measurement of the third-order non-linear susceptibility.
Through FWM experiments, modulated pump (1,556 nm) and
continuous-wave probe (1,536 nm) signals are injected into the
device in a measurement configuration similar to that used in refs
23,51. The modulated pump drives the excitation of Brillouinactive phonons over a wide range of frequencies as the pump
modulation frequency is swept. The non-linear response of the
device is then analysed by heterodyne measurement of optical
tones imprinted on the disparate probe wavelength due to a
coherent combination of the Brillouin and third-order electronic
4
non-linear susceptibilities (that is, through FWM). These
sidebands are then analysed as distinct RF tones through
heterodyne interferometry. In contrast to the approach of refs
23,51, this heterodyne approach allows the Stokes and anti-Stokes
signatures to be resolved separately. For further details, see the
Methods section.
As seen from Fig. 4, clear signatures showing the non-linear
Brillouin response were observed by measuring the intensity of
non-linearly induced sidebands imprinted on the probe, as the
pump modulation frequency was swept from 1 to 18 GHz. The
spectra in Fig. 4 were obtained by integrating the RF power
produced by heterodyne detection of the probe signal (including
both Stokes and anti-Stokes sidebands) over a discrete set of highfrequency RF bands using RF filters. To remove the frequency
dependence of the detection system and to more clearly exhibit the
sharp Brillouin resonances, the spectra in Fig. 4 were normalized to
those of an identical optical waveguide without a Brillouin-active
region. Each waveguide produces a series of regularly spaced
Brillouin resonances analogous to those identified in Fig. 2.
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Pump
IM
p ± Ω/2
1,556 nm
BC
RFG
p –Ω/2, p +Ω/2
pr
Ω
Ω
p –Ω/2, p +Ω/2
pr, pr ± Ω
pr, pr ± Ω
Probe
IF
pr
1,536 nm
PC
WDM
70:30
pr
pr+Δ
30:70
RF-PM / SA
AOM
PC
RFD
Figure 3 | Heterodyne two-colour pump–probe apparatus. Schematic diagram of the apparatus used to measure the Brillouin non-linearity of the BAM
waveguide. The non-linearly induced phase changes imparted to the probe beam (1,536 nm) by the waveguide device are detected using heterodyne
interferometer, whereas a modulated pump beam (1,556 nm) produces driven excitation of the Brillouin-active phonon modes. Components of the
apparatus are labelled as follows: ISO, isolator; PC, polarization controller; IM, intensity modulator; RFG, RF generator; BC, bias controller; WDM,
wavelength division multiplexer; AOM, acousto-optic modulator; RFD, RF driver; IF, interference filter; SA, spectrum analyser; RF-PM, RF power meter.
m=1
m=2
m=3
m=4
m=5
m=6
w
m=7
Normalized output signal (a.u.)
3.8
w (μm)
2.8
1.8
0.8
0
3
6
9
12
15
18
Modulation frequency (GHz)
Figure 4 | Spectra of non-linear Brillouin spectra obtained through heterodyne FWM measurements. The resonant Brillouin signatures produced by
several BAM waveguides are displayed for waveguide dimensions w ¼ [0.8, 1.8, 2.8, 3.8] mm. Each trace is obtained by normalizing the signal produced by
each Brillouin-active waveguide to that of an identical reference silicon waveguide (one that is not Brillouin active) under identical experimental conditions.
The dashed blue circles shown atop the experimental traces show the numerically computed frequencies of each Brillouin-active phonon mode as the
waveguide dimension, w, varies. The upper right inset is a schematic geometry of the BAM waveguide. Each waveguide has the resonant modes labelled by
a mode index, m, as in Fig. 2.
Because of the spatial symmetry of the optical force distribution,
only phonon modes with even displacement symmetry with
respect to the waveguide core produce efficient Brillouin coupling.
The different resonant signatures are colour coded (red, green, blue
and so on) to indicate the mode order (1st, 2nd, 3rd and so on) of
each phononic resonance as the Brillouin spectrum shifts with
waveguide dimension. All 17 experimentally observed resonances
between 1 and 18 GHz showed good agreement with simulated
mode frequencies over the range of device dimensions. The
simulated modal frequencies are displayed as dashed curves atop
the experimental data. Figure 4 reveals that a variation of the cavity
dimension allows precise placement of Brillouin resonances at
virtually any frequency from 1 to 18 GHz, for an unprecedented
degree of non-linear tailorability. For example, the m ¼ 2 resonance
(green) is shifted from 3.7 to 17 GHz, as the cavity dimension, w,
varied from 3.8 to 0.8 mm. Although the bandwidth limitations of
our apparatus did not permit measurements beyond 18 GHz, strong
Brillouin resonances are expected at 25 GHz and higher frequencies.
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Anti-stokes
Stokes
Fitting
1.2
Fitting
0.8
0.4
6.16
6.18
6.17
6.19
Frequency (GHz)
|γSBS| (W–1 m–1)
ES and RP combined
Electrostriction
Radiation pressure
Thermoelastic coupling
1,000
750
|γSBS| (W–1 m–1)
4
500
2
250
0
Q –factor
6
|γSBS|/|γFWM|
6.18
6.19
6.17
Frequency (GHz)
Normalized
output signal
(a.u.)
0.0
6.16
0
Theory
1,500
9
Measurement
6
1,000
500
3
0
2,000
0
|γSBS|/|γFWM|
Power (×10–9, a.u.)
ARTICLE
1,000
0
1.28
3.72
6.18
8.70
11.31 13.83
Resonant frequency (GHz)
16.30
Figure 5 | Characteristic spectral Brillouin line shapes and nonlinear
coefficients obtained from both experiments and simulations. (a,b)
Spectrally resolved Stokes and anti-Stokes Brillouin lines shapes,
respectively, for the m ¼ 3 resonance of w ¼ 3.8 mm BAM waveguide. The
theoretical fit (red line) obtained using the line shape derived in
Supplementary Note 2 are shown as red curves atop the experimental data
(circles). (c) Normalized heterodyne signals measured by the RF power
meter for w ¼ 3.8 mm. (d) Simulated contributions of radiation pressure
(blue bar), ES forces (orange bar) and thermoelastic coupling (violet bar) to
the total Brillouin non-linear coefficient (black bar) are numerically
calculated for w ¼ 3.8 mm for a fixed phononic Q of 1,000. (e) Comparison
between the experimentally obtained (pink circle) and the theoretically
calculated (green bar) SBS gain coefficients when experimentally measured
quality factor of each resonant mode is incorporated within simulations.
(f) Measured Q-factor of each resonant mode versus frequency for each
resonance of the w ¼ 3.8 mm BAM waveguide, corresponding to modes
m ¼ 1,2,y7 identified in Fig. 2.
Quantitative analysis of the Brillouin non-linearity. Close
examination of the resonance signatures in Fig. 4 reveals a Fanolike line shape produced by each Brillouin resonance, from which
the magnitude of the Brillouin non-linear coefficient, gSBS, can be
obtained. This line shape can be more clearly seen from the highresolution spectral scans of Fig. 5a,b, which show the line shape of
a characteristic Brillouin resonance (f ¼ 6.185 GHz, with w ¼
3.8 mm) decomposed into its Stokes and anti-Stokes components.
These data were obtained by spectrally resolving the distinct
heterodyne tones of the Stokes and anti-Stokes signals using a
high-resolution RF spectrum analyser (SA) as the pump modulation frequency was swept. This asymmetric line shape results
6
from the coherent interference between the Brillouin and electronic Kerr non-linearities of the waveguide. Involvement of
electronic Kerr non-linearities at the Stokes and anti-Stokes frequencies occurs due to cross-phase modulation between the
pump and probe beams within the silicon waveguide core. Note
that the fibre apparatus yields a negligible contribution to the
measured Brillouin and Kerr non-linearities of the device.
To precisely determine the magnitude of the Brillouin nonlinear coefficient, gSBS, relative to the intrinsic Kerr non-linear
coefficient gK and the non-linear free-carrier dispersion coefficient gFC from these data, the non-linear coupled amplitude
equations were formulated to derive the functional form of the
Stokes and anti-Stokes line shapes (see Supplementary Note 2).
As SBS is a resonant effect, its non-linear coefficient takes on a
Lorentzian line shape centred about each Brillouin-active phonon
mode. In contrast, the electronic Kerr non-linearities are nonresonant at 1,550 nm wavelengths, yielding a frequency-independent non-linear coefficient. As in the fibre-based studies of Wang
et al.40, the frequency-dependent interference between the Kerr
and Brillouin effects produces the asymmetric (Fano-like) line
shape observed in Fig. 5a,b. However, it should be noted that our
experimental arrangement is distinct, leading to a different set of
coupled amplitude equations. In addition, non-linearly generated
free carriers in silicon are responsible for the dissimilar line
shapes of the Stokes and anti-Stokes orders, and a larger nonlinear background for frequencies below 2 GHz under our
experimental conditions. As the free-carrier effects roll off at
high frequency, the Kerr responses at 16 GHz are used as a
reference to determine the magnitude of the Brillouin non-linear
coefficient, similar to that in ref. 52.
On the basis of the coupled amplitude model described in the
Supplementary Note 2, the magnitude of the Brillouin non-linear
coefficient, gSBS, is extracted from the experimental line shape of
both the Stokes and anti-Stokes signatures of each resonance of
the w ¼ 3.8 mm BAM waveguide. Seven resonances, spanning
frequencies from 1.28 to 16.30 GHz, are shown in Fig. 5c. The
peak value of |gSBS|/|gK| and the phononic Q-factor of each
resonance extracted from experiments (including separately
resolved Stokes and anti-Stokes signatures) are shown Fig. 5e,f
respectively. The peak value of the Brillouin non-linear coefficient
at 1.28 GHz is found to be 6.18 times larger than the Kerr
non-linear coefficient of the waveguide (or |gSBS|/|gK| ¼ 6.18).
From the established non-linearities of silicon53, |gK| of
188±34 W 1 m 1 was found for BAM waveguides with
w ¼ [1.8, 2.8, 3.8] mm (for further details see Supplementary
Note 2)54,55. From this relative measurement, the Brillouin
non-linear coefficient is found to be j gSBS j ffi 1; 164 244 W 1 m 1 over the Brillouin-active region of the BAM
waveguide. Moreover, as the Brillouin non-linear coefficient
is related to the Brillouin gain as 2|gSBS| ¼ GSBS, this nonlinearity corresponds to a forward SBS gain of
GSBS ffi 2; 328 488 W 1 m 1 . Note that much of the ±18%
and ±21% uncertainty assigned to |gK| and |gSBS| values,
respectively, arise from the (±15%) uncertainty in the
measured value of the Kerr non-linearity of silicon53. Despite
the fact that this non-linear response is the aggregate of an
ensemble of 26 distinct Brillouin-active suspended regions
fabricated along the length of the waveguide, remarkably high
mechanical Q-factors (B1,000) are produced for phonon
frequencies of 1.28 to 16.3 GHz.
Comparison with theory. For comparison with experiments, fullvectorial three-dimensional multi-physics simulations were performed through coupled optical force and elastic wave COMSOL
models following the approach outlined in ref. 41. The distinct
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contributions of ES forces (orange), radiation pressure (blue) and
thermoelastic expansion (violet) to the total SBS nonlinear
coefficient (black) are shown in Fig. 5d for each phonon resonance. Here a fixed mechanical Q-factor of Q ¼ 1,000 is assumed.
Note that negligible contribution to the Brillouin coupling is
produced by thermoelastic response at these GHz frequencies due
to the slow thermal time constant of this system (for further
details, see the Supplementary Discussion). The magnitude of the
Brillouin coefficient, |gSBS|, scales quadratically with optical force,
yielding a non-linear addition of the radiation pressure and
electrostrictively induced couplings to the overall Brillouin gain as
seen in Fig. 5d (ref. 41). The total Brillouin non-linearity, which is
almost exclusively driven by radiation pressure and
electrostriction, slowly decreases with increasing resonant
frequency as seen in Fig. 5d. A larger variation in Brillouin
non-linearity is seen from the experimental data (circles of
Fig. 5e) than from simulations (black bars of Fig. 5d) due to the
variation of the measured phononic Q with frequency (Fig. 5f).
However, when the frequency dependence of measured Q-factors
is included in simulations (Fig. 5f), good agreement between
simulations and experiments are obtained over the entire
frequency range (green bars of Fig. 5e).
Both the highly localized electrostriction and radiation pressure
force distributions within the waveguide core yield a frequencydependent Brillouin gain (seen in Fig. 5d) exhibiting a significant
departure from conventional backwards SBS processes involving
bulk acoustic waves. In contrast to the rapid 1/O roll off of
Brillouin gain with phonon frequency found through backward
SBS41,56,57, the experimental (and simulated) Q-factor
normalized Brillouin coefficient varies by less than 40% in
magnitude over the entire 1–16 GHz frequency range. Unlike
conventional systems where the overlap between the optical force
distribution and the phonon mode profile is largely frequency
independent, the complex double-lobed spatial force distributions
in the core of the silicon waveguide produce a frequencydependent overlap with various phonon modes, reshaping the
frequency dependence of Brillouin coupling. The effect of spatial
force distribution on the frequency dependence of coupling can
be clearly seen by comparing the computed contributions of
electrostriction and radiation pressure to the Brillouin gain of
Fig. 5d. Although the radiation pressure contribution diminishes
quite rapidly with frequency, the ES component varies by only a
few per cent over 1–16 GHz frequency range. The higher
bandwidth of ES coupling results from the higher spatial
frequencies of the ES force distribution. Consequently, the
relatively flat Brillouin gain produces efficient photon–phonon
coupling over an unprecedented frequency range. The magnitude
and frequency dependence of the measured Brillouin coupling,
and their good agreement with simulations, all provide strong
evidence of the important role of both electrostriction and
radiation pressure within these BAM waveguides.
Stimulated Brillouin-scattering gain measurement. The series
of Brillouin resonances generated by the w ¼ 3.8 mm device provide insight into the bandwidth and frequency dependence of the
Brillouin coupling, though a larger overall Brillouin non-linearity
can be achieved with a higher degree of phonon confinement
(that is, smaller values of w). Figure 6a shows the Stokes and antiStokes spectral line shapes obtained by through-measurement of
the w ¼ 0.8 mm BAM waveguide device. In contrast to the
w ¼ 3.8 mm device, several sharp spectral features, consistent with
high Q-factor (QB1,500) phononic resonances, are observed
within the central Brillouin line shape, suggesting significant
b
6
Power (×10–9, a.u.)
Anti-stokes
Fitting
Stokes
Fitting
4
2
0
5.63
5.67
5.71
5.63
5.67
RF frequency (GHz)
Normalized transmittance
a
Pp = 12 mW Pp = 14 mW Pp = 20 mW
1.09
1.06
1.03
1.00
5.71
d
Data
Fitting
5.65 5.7
5.65 5.7
5.65 5.7
RF frequency (GHz)
c
Pp = 12 mW Pp = 14 mW Pp = 20 mW
1.0
Normalized transmittance
Peak amplification
1.1
Stokes
Anti-stokes
0.9
10
15
Pump power (mW)
1.00
0.97
0.94
0.91
20
Data
Fitting
5.65 5.7
5.65 5.7
5.65 5.7
RF frequency (GHz)
Figure 6 | Normalized transmittances of Stokes and anti-Stokes Brillouin signals and characteristic spectral Brillouin line shapes. (a) Spectrally
resolved Stokes and anti-Stokes Brillouin lines shapes, respectively, obtained through heterodyne FWM experiments. (b,c) Normalized transmittances of
Stokes and anti-Stokes Brillouin signals, respectively, for the m ¼ 1 resonance of d ¼ 0.8 mm BAM waveguide for the pump powers of 12, 14 and 20 mW. (d)
Peak amplification (absorption) of Stokes (anti-Stokes) signals versus pump power obtained from the line shapes of b and c.
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p
ASE
IF
IF
S
EDFA
S
p,S
S
Power
PC
p,AS
Power
or
EDFA
Power
p,S
Power
Power
Tunable laser
p,S
S
SA
Figure 7 | Experimental gain measurement apparatus used to measure the Brillouin gain spectrum of the BAM waveguide. ASE signal (ns) beam is
combined with the pump (np) beam, and both beams are coupled into and out of the waveguide with d ¼ 0.8 mm using lensed fibres. Two identical
interference filters (IFs) are used to create unbalanced input/output signals. The pump frequency is located at the 3-dB band edge of the IFs, higher
frequency for measuring the Stokes signal and lower frequency for the anti-Stokes signal. The strong pump beam induces the SBS gain at resonant
frequencies, and the interference signal between the pump and ASE fields is monitored by an RF spectrum analyser (SA). PC, polarization controller; EDFA,
erbium-doped fibre amplifier.
inhomogeneous broadening due fabrication non-uniformities in
this case. A fit of the aggregate Brillouin line shape using a single
Lorentzian oscillator model yields is seen in Fig. 6a, yielding GSBS
and Q-values of GSBS ffi 4; 150 872 W 1 m 1 and QD280.
However, uncertainty in the form of inhomogeneously broadened
line shape made it difficult to obtain a high confidence estimate of
the Brillouin non-linearity in this case, prompting us to explore
Brillouin non-linearities through direct measurement of Brillouin
gain.
Experimental studies of Brillouin gain, performed by injecting
strong pump and weak signal fields into a Brillouin-active
waveguide (w ¼ 0.8 mm), are shown in Fig. 7. A low spectralintensity amplified spontaneous emission (ASE) probe signal
(centre wavelength: 1,552.94 nm; bandwidth: 50 GHz) was used
in conjunction with a high-intensity pump laser (lp,S ¼
1,552.723 nm or lp,AS ¼ 1,553.158 nm) to perform Brillouin gain
measurements about the Stokes and anti-Stokes frequencies,
respectively. The spectral power density of the ASE signal beam
was measured by monitoring the heterodyne interference between
the pump and signal fields with a receiver and an RF SA for
frequencies about the Brillouin resonance (v ¼ 5.68 GHz).
The transmitted ASE power spectral density for higher pump
powers are normalized to the power spectral density at lower
pump powers (2.6 mW) to observe the power-dependent form of
the Stokes and anti-Stokes line shapes. The normalized Stokes
and anti-Stokes transmittances for Pp ¼ 12, 14 and 20 mW are
shown in Fig. 6b,c, respectively. The finer structure produced by
inhomogeneous broadening is not visible because of the smaller
signal-to-noise ratio obtained by this method. Lorentzian fits of
the Stokes and anti-Stokes line shapes yield a Q-factor of B300,
indicating significant inhomogeneous broadening in this case. As
the anti-Stokes process involves transfer of energy from the signal
to the pump beam, the anti-Stokes signature (Fig. 6c) exhibits
depletion instead of gain as shown in Fig. 6b. The theoretical fits
(red line) performed using the line shape derived in Supplementary Note 3 are shown as red curves atop the experimental data
(blue circles). In the small signal limit, which we explore through
these experiments, the SBS gain is proportional to the pump
power, and the amplification (and depletion) at resonant centre
frequency is linear with the pump power as shown in Fig. 6d. A
total effective forward SBS gain of GSBS ffi 2; 750 1; 200 W 1 m 1 was extracted by fitting the data in Fig. 6b,c as
described in the Supplementary Note 3. This measurement also
shows good agreement with the simulated value of Brillouin gain,
GSBS ffi 2; 570 540 W 1 m 1 . Note that these values of
Brillouin gain are more than a factor of 10 larger than those
obtained by treating the Brillouin non-linearities of silicon as a
bulk medium property, providing strong evidence of the role of
boundaries in shaping non-linearity at subwavelength scales.
8
These measurements clearly demonstrate a gain coefficient that is
over 1,000 times larger than recent demonstrations of forward
SBS in fibres12, and several times larger than the Raman gain
produced by silicon19,21, making Brillouin non-linearities the
dominant third-order non-linearity in these silicon waveguides.
Discussion
Although slight inhomogeneous broadening due to device
dimension variability is observable from some of the measured
Brillouin line shapes of various devices, consistent Brillouin gain
and high Q-factor Brillouin resonances are found across the
fabricated wafers. The nearly frequency-independent Q-factors
observed through experiments suggest that factors other than
intrinsic material dissipation limit the Q-factors observed
here58,59. Hence, significant further enhancements in Q-factor
and Brillouin gain should be attainable with device refinement
and tighter dimensional control.
In conclusion, we have made the first demonstration of
travelling-wave Brillouin non-linearities and Brillouin gain in
silicon waveguides through a novel class of hybrid photonic–
phononic waveguides. Through quantitative measurements,
forward SBS non-linear susceptibilities were measured to be
more than 1,000 times stronger than any previous waveguide
system. Multi-physics simulations reveal that this strong photon–
phonon coupling is produced by a constructive combination of
ES forces and radiation pressures at nanoscales. The emergence of
large radiation pressure-induced couplings represents a new form
of boundary-induced Brillouin non-linearity41,48,49 and a new
regime of boundary-mediated Brillouin coupling that arises in
subwavelength structures. This novel waveguide geometry enables
independent control of phononic modes and optomechanical
driving forces to yield tailorable Brillouin coupling over
exceptionally wide bandwidths. Simultaneous coupling to
numerous transverse phonon modes yields a relatively flat
Brillouin gain over this entire 1–18 GHz frequency range. We
have demonstrated that structural tuning of phononic resonances
from 1 to 18 GHz with high-quality factor (41,000) yields
tailorable non-linear optical susceptibilities due to the coherent
interference of Kerr and Brillouin effects. In this system, the
wideband nature of this photon–phonon coupling results from
the highly localized optical forces produced within the nanoscale
waveguide. These wideband and high-frequency (18 GHz)
characteristics were achieved without the need for ultra-highresolution lithography, significantly extending the frequency
range of chip-scale photon–phonon coupling over state-of-theart cavity optomechanical technologies.
Efficient coupling between a continuum of optical and
phononic modes through such chip-scale travelling-wave
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Brillouin processes opens up a host of wideband signal-processing
capabilities with CMOS-compatible silicon photonics, including
pulse compression13, pulse and waveform synthesis12,14,15,44,
coherent frequency comb generation12,15,16, variable bandwidth
optical amplifiers and filters44–46, and coherent beam-combining
schemes47. Travelling-wave Brillouin non-linearities can also
produce optical phase conjugation60 and opto-acoustic isolators18
that are necessary to reduce signal distortions and eliminate
parasitic reflections on silicon chips. In addition, the highly
controllable nature of the phonons emitted by this hybrid
photonic–phononic system could enable forms of coherent
information transduction through travelling-wave processes that
are complementary to recent cavity optomechanical systems. As
efficient Brillouin-based photon–phonon conversion is possible
over wide bandwidths (420 GHz), and the Brillouin-emitted
phonons can be guided and manipulated on chip, hybridization
of Brillouin device physics with silicon photonics, CMOS and
microelectromechanical systems could provide a host of new
coherent signal-processing technologies.
Methods
Fabrication methods. The silicon waveguides were patterned in a silicon-oninsulator with at 3,000 nm oxide undercladding using an ASML deep UV scanner,
and etched in an AMAT DPS polysilicon etch tool. Following resist strip and
standard post-etch and pre-diffusion cleans, LPCVD Si3N4 of 300 nm thickness was
deposited in an SVG series 6000 vertical. A chemical–mechanical polish was used
to preferentially thin conformal nitride atop Si waveguide. Hot phosphoric acid
etch was used to clear the remaining nitride atop the silicon waveguide. The net
result is the waveguide cross-section seen in Fig. 1. The nitride layer was then
patterned to form the air slots seen in Fig. 1. Facet cuts for fibre access were created
by patterning thick resist using a 1 mask in a SUSS MA-6 contact aligner and
employing deep-RIE etch. The oxide undercladding was then released in a 49%
hydrofluoric acid etch.
Experimental methods. The pump beam (at 1,556 nm) is modulated using a
Mach-Zehnder intensity modulator. Mutually incoherent light from another
distributed feedback laser at 1,536 nm is used as the probe beam. The probe beam
splits into two paths to form a heterodyne interferometer. In the upper arm of the
interferometer, the probe beam is combined with the pump beam using a wavelength division multiplexer. Both pump and probe beams are coupled into and out
of the waveguide using lensed fibres. The pump wave exiting the device is blocked
by an interference filter such that no pump light could be detected. The probe beam
is frequency shifted by D ¼ 165 MHz using an acousto-optic modulator in the
lower arm of the interferometer to form the local oscillator for heterodyne
detection. In traversing the Brillouin device in the upper arm of the interferometer,
the pump- beam produces non-linearly sidebands (or a signal) on the probe beam.
At the output of the interferometer, local oscillator is then mixed with the probe
beam and signal using a 30:70 directional coupler, and detected using a high-speed
(18 GHz) receiver. The RF signals produced through detection are then measured
with either an RF power meter or an RF spectrum analyser. Because of the 165 MHz frequency offset of the local oscillator, the Stokes and anti-Stokes signatures can be observed as separate tones in the RF SA, with a total frequency
separation of 330 MHz. By scanning the drive frequency of the RF signal generator
while measuring either RF power or RF spectrum, detailed analysis of the Brillouin
response of the system is made. A fibre-to-chip coupling loss of 8 dB and waveguide propagation loss of 7 dB cm 1 were estimated through waveguide cutback
measurements. Pump and probe powers internal to the waveguide are estimated to
be 6.5 mW and 9.6 mW, respectively.
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Acknowledgements
Sandia Laboratory is operated by Sandia Co., a Lockheed Martin Company, for the US
Department of Energy’s NNSA under contract number DE-AC04-94AL85000. This work
was supported by the DDRE under Air Force contract number FA8721-05-C-000, the
MesoDynamic Architectures programme at the DARPA under the direction of Dr Jeffrey
L. Rogers, and Sandia’s Laboratory Directed Research and Development programme
under Dr Wahid Hermina. We thank Marin Soljačić, Ryan M. Camacho and Ihab
El-Kady for helpful technical discussions involving phononic systems, optomechanics
and non-linear interactions. We thank Jack Harris, Jack Sankey and Benjamin Zwickl
for helpful discussions concerning thermoelastic dissipation in silicon nitride membranes. We are grateful to Douglas Trotter for guidance through fabrication process
development and Whitney Purvis Rakich for careful reading and critique of this
manuscript.
Author contributions
All authors made important contributions to this work. R.J. and A.S. fabricated the
waveguide devices. P.R. designed devices with assistance of R.H. and Z.W. W.Q. and
Z.W. developed multi-physics simulations. W.Q., Z.W., J.C. and P.R. performed
numerous device simulations to understand various aspects of experiments. H.S., W.Q.,
Z.W. and P.R. developed analytical models to describe device non-linearities and Brillouin coupling. H.S., J.C. and P.R. developed the experimental techniques. H.S. conducted experiments with assistance of P.R. H.S., Z.W. and P.R. conceived and designed
the experiments. All authors contributed to the writing of this paper.
Additional information
Supplementary Information accompanies this paper at http://www.nature.com/
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Competing financial interests: The authors declare no competing financial interests.
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How to cite this article: Shin, H. et al. Tailorable stimulated Brillouin scattering in
nanoscale silicon waveguides. Nat. Commun. 4:1944 doi: 10.1038/ncomms2943 (2013).
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